An implicit method for coupled flow-body dynamics

We propose an efficient method for computing coupled flow–body dynamics. The time-stepping is implicit, and uses an iterative method (preconditioned GMRES) to solve the flow–body equations. The preconditioner solves a decoupled version of the equations which involves only the inversion of banded matrices, and requires a small number of iterations per time step. We use the method to probe the instability to horizontal motions of an elliptical body with simple vertical motions: flapping and rising. In both cases a linear instability to horizontal motion sets in above a critical Reynolds number, leading to a stable oscillatory state. The pressure forces play a destabilizing role against the stabilizing viscous forces, with oscillatory time scales set by either external flapping or the intrinsic flow–body coupling. The latter lowers the instability threshold in Reynolds number. 2008 Elsevier Inc. All rights reserved. PACS: 47.11. j; 47.11.Bc; 47.20.Ky; 47.63.M